【土木計画学研究・論文集 Vol.26 no.5 2009年9月】
A FRAMEWORK FOR REAL-TIME CRASH PREDICTION: STATISTICAL APPROACH VERSUS
ARTIFICIAL INTELLIGENCE*
by Moinul HOSSAIN** and Yasunori MUROMACHI***
1. Introduction
The attempts to predict crashes on freeways through statistical modeling involving capacity driven measures of traffic
flow (e.g., AADT) and road geometry have spanned for more than two decades. However, success in crash prediction
involving these static data has so far been limited. In recent times, some researchers made efforts to accommodate the
weather conditions and seasonal effects to better predict crashes through time series analysis. So far, these models have
shown their incapability to accommodate the ever complex human factors, which, to a great extent, are believed to be
directly or indirectly responsible for most of the crash cases. Moreover, the prediction outcome of these models is long-term
and mainly used to forecast yearly crash, their seasonal variation, identify black-spots or to assess the impact of road
improvement initiatives, etc. However, these models overlook the fact that crash can happen even on geometrically correct
roads with excellent weather condition due to human factors. One of the latest additions to the crash prediction modeling is
the approach to predict crashes based on real-time traffic data which considers the human factors in macroscopic level from
the traffic engineering perspective. The assumption in these models is, instantaneous traffic flow data are indirect
representation of the human factors. The concept of real-time crash prediction modeling is gaining momentum due to its
proactive nature of application and the growing implementation of ITS, which ensures the future availability of real-time
traffic data. However, being at its primitive stage and due to scarcity of past real-time data, the present models are yet
theoretical and largely prone to unrealistic data requirements and lack of reliability. Moreover, there has not been any well
established norm for modeling approach as well. Some researchers preferred using well known statistical methods while
some others opted for artificial intelligence based methods. However, the basic concept in modeling crash in real-time has
remained the same, in which, the traffic flow data are separated into two groups – condition leading to crash and normal
condition, based on specified assumptions, and then future traffic flow data are evaluated to estimate how likely they are to
fit into each of these groups. As crash is considered as a rare event, these models need to have the capability of being
frequently updated as soon as new data are available. In future, we can expect that the models will also incorporate nontraffic flow variables to attain higher prediction accuracy. Moreover, the operation of these models is highly dependent on
the reliability of the detectors, and hence, is expected to predict even when some data are missing. Considering these
requirements, in this paper, we have investigated the applicability of Bayesian Network (BN), a popular real-time prediction
method in the field of information science, as a probable method to predict crash in real-time. Bayesian Network is a
graphical probabilistic modeling approach which can be calibrated in real-time with limited effort, can handle integration of
new variables in future with little effort and also suitable in predicting with missing data. Although its inherent features are
suitable for real-time crash prediction, it is important to make sure that BN exhibits satisfactory level of accuracy in
predicting crashes, too. For this, after developing the model with BN we developed another model with Binary Logistic
Regression and used it as a baseline to investigate the prediction capability of BN.
We have organized the paper into four parts. In the first part, we conducted a literature review on real-time crash
prediction models and explain the steps involved in modeling as well as making prediction in practical situation. Afterwards,
we provided a short introduction to BN, clarifying the concepts important for the readers for understanding the paper. Then
we have developed a prototype real-time crash prediction model with artificially generated data and compared its
performance in crash prediction with Binary Logistic Regression. Lastly, we discussed the results, elaborated the limitations
of the study and evaluated the possibilities of using BN for real-time crash prediction.
2. Literature Review
The study by Oh et al.1)-3) was the first of its kind to assess the possibility to classify a traffic condition as crash prone to
estimate the likelihood of potential crashes. In that study, they separated traffic dynamics into two categories – disruptive (or
hazardous) and normal. A hazardous traffic condition is defined as that potentially leading to a crash occurrence whereas a
normal traffic condition does not instigate crashes. Normal condition in these studies was specifically defined as a 5 minute
* Keywords: real-time crash prediction, logistic regression, Bayesian Network
** Graduate Student, M. Eng., Dept. of Built Environment, Tokyo Institute of Technology
(Nagatsuta-machi 4259,Midori-ku, Yokohama, Kanagawa 226-8502, Japan, Telefax: +81-(0)45-924-5524, Email: moinul048i@yahoo.com)
***Member of JSCE, Dr. Eng., Dept. of Built Environment, Tokyo Institute of Technology
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period occurring at 30 minutes prior to the crash and the disrupted condition was defined as the 5 minute time period just
before the crash. A total of 52 crashes had adequate real-time traffic data to be matched with. Later on, they employed t-test
on the mean and deviation of three variables – occupancy, flow and speed, to identify the crash indicators. However, there
was no suggestion explaining if they have tested the data for normality as t-test is applicable only with the assumption that
the data follow normal distribution. Oh et al.2) identified standard deviation of speed to be the most significant variable
although most of the variables came out as significant in the t-test. Later, they defined the two traffic conditions with two
probability density functions (PDF) and used those to identify the posterior probability of a traffic condition to belong to
either of these two traffic conditions and determine crash probability thereby. In their latest study (Oh et al.3)) they also used
average of occupancy as a predictor. In their second study (Oh et al.2)) they employed a nonparametric Bayesian approach to
identify the real-time crash likelihood. In the latest study (Oh et al. 3)) they applied Probabilistic Neural Network (PNN) to
accomplish their estimation purpose. Lee et al.4)，5) conducted two studies to predict crash risk in real time where the second
study basically reduced the number of assumptions made in the first study to make it more acceptable. In their latest model
they selected speed variations along a lane, traffic queue and traffic density at given road geometry, weather condition and
time of the day as predictors and applied aggregated first order log-linear model to predict crash. The initial study by AbdelAty et al.6) concentrated on classifying speed patterns to predict crashes in real-time. Their later study (Abdel-Aty et al.7))
incorporated road geometry into the model using Generalized Estimating Equations for correlated data. This research was
the first of its kind where a series of crash and non-crash traffic classification analysis were conducted to identify the
predictors. They used Probabilistic Neural Network method to separate traffic patterns leading to crash from those not
leading to crash. The variables found significant in their model were mean and variance of volume, occupancy and speed.
Later on, they employed Generalized Estimating Equations to predict crashes. The study further calculated the false alarm
rate, too. It was suspected that Abdel-Aty et al.'s 6)，7) model may generate high false alarm as they considered the traffic
variables independently ignoring their interactions. The research project by Luo and Garber 8) is the latest addition in the
attempt to predict crashes in real-time. They commenced their research with intensive investigation of previous research
studies. Luo and Garber 8) analyzed each crash case independently to identify crash leading patterns and factors describing
the patterns. Like Abdel-Aty et al. 6)，7), they also suggested mean and variance of occupancy, speed and volume to be
suitable for predicting crashes in real-time. However, they limited their study within identifying traffic patterns
distinguishing crash and non-crash situations. They applied three pattern recognition methods: K-means clustering method,
Naive-Bayes method and Discriminant Analysis and compared the outcomes. Apart from Naive-Bayes method, no other
method in their study reached an overall 50% prediction success. We have summarized the overall modeling approach and
the hypothetical work-flow of a real-time crash prediction model in Figure1.
Figure 1: Modeling approach and work-flow of a real-time crash prediction model
In all of the aforementioned prominent studies on real-time crash prediction, they used statistical measures of one or
more of the traffic flow variables – speed, flow and occupancy, in real-time. They had high similarity in overall modeling
approach, too. All these studies were conducted on freeways and most of them clearly fixed the section of the road under
consideration for study to eliminate the influence of varying road geometry. All the studies followed the norms of Oh et al.1)3)
by separating the traffic condition into two parts – leading to crash and normal. However, they had differences in defining,
specially the normal traffic condition. In case of Oh et al.1)-3), they defined normal traffic condition as a 5 minute traffic
flow data collected 30 minutes prior to crash on the same day when the crash took place. However, Abdel-Aty et al.'s 6)，7)
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argued that this classification of normal traffic condition may be not be justifiable and assumed that traffic condition for a
specific time of a day remain similar to that of same day, same time for different weeks of the year. They defined the normal
traffic condition as a 5 minute traffic flow data for the same time period for the same days through out the year. Apart from
this, the main major difference among these proposed models have been the method of modeling. Table 1 summarizes our
findings from the literature review.
Table 1: Real-time crash prediction models at a glance
Sample
Study
Motivation
Variable
Method
Evaluation
Outcome
Size
Standard deviation of
random sampling
Proactive
Probabilistic
Oh et al. (3)
52
speed, average
from the model
Conclusive
Road Safety
Neural Network
occupancy
building data
standard deviation of
speed, difference is
Proactive
1st order logLee et al. (5)
234
speed between
Model Statistics
Conclusive
Road Safety
linear Models
upstream &
downstream, density
49 random
variance of speed and
samples mutually
Abdel-Aty et Proactive
Probabilistic
149
volume, mean of
exclusive from the Conclusive
al. (6)
Road Safety
Neural Network
speed
model building
data
Luo et al. (8)
Proactive
Road Safety
& Crash
Phenomena
391
various combination
of descriptive
statistics of speed,
flow and occupancy
K-cluster mean,
Naïve Bayes,
Discriminant
Analysis
N/A
Inconclusive
As the idea of predicting crash in real-time is in its infancy, neither of the studies recommended their models to be
directly used for practical situation. They emphasized that due to lack of data, it is difficult to develop the initial model with
acceptable accuracy and these models need to be calibrated frequently with new crash and non-crash data. They also
mentioned that in future the generalized models will be required to have capabilities to incorporate variables related to road
and environment. In fact, Abdel-Aty et al.7) developed their latest model incorporating weather and road geometry related
variables into their previously developed model. The studies also suggested that a practical real-time crash prediction model
must not be susceptible to missing data as detectors may often fail to yield all the data for each time interval. However, so
far the focus of the previous studies have been on developing or improving the framework and choosing the method to
improve the crash prediction capability rather than the model's suitability for practical use. In this study, we bridge this gap
by choosing BN as the modeling method, which is widely known for its flexibility in future calibration, present data
requirements and features to incorporate new variables easily in future. However, as prediction capability is another
indispensable requirement, we investigate if BN can yield satisfactory prediction accuracy by comparing its performance
with Binary Logistic Regression.
3. Fundamentals of Bayesian Network (BN)
Bayesian Network (BN) can be defined as an acyclic directed graph (DAG) which defines a factorization of a joint
probability distribution over the variables that are presented by the nodes of the DAG, where the factorization is given by
the directed links of the DAG9). BN is a graphical modeling method and it is presented with a graph and a basic equation.
The graph consists of two parts as well – the nodes and the arcs. The variables in a BN are represented as nodes and their
inter-relationship is represented with the arcs. For example, in Figure 2, a problem domain is represented with five variables
– A, B, C, D and E, where B is caused by D, E is caused by B and C is caused by A and B together. Thus, A and B are the
parent nodes of C and C is their common child node, D is the parent node of B and B is its child node and so on.
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Figure 2: A Simple Bayesian Network
The inter-relationships of the variables are represented by drawing arcs from the parent nodes to the child node. If a BN
contains 'n' number of variables, then we can represent the complete problem domain as Equation 1.
(1)
In order to specify a BN, we need to provide the probability (or conditional probability) distributions of all the nodes.
Thus, as we have five variables in our example, if each variable is dichotomous, i.e., had only two states then we are
expected to need 25-1, or, 31 joint probabilities. However, the architecture of BN suggest that each network can be presented
with the probabilities of each node who do not have any parent node and the conditional probabilities of the child nodes
with respect to their immediate parent nodes only. Thus, Equation 1 can be re-written as Equation 2 for our example.
(2)
Now, in future, if we think that only the behavior of variable B and D has changed that may require the model to be
calibrated, we need to collect data for only P(B), P(D) and P(B|D) to recalibrate the whole model. Thus, the same model can
be built with data of different time period. Moreover, in course of time, if we find that it is necessary to incorporate a new
variable F which influences both A and B, then we can update the model by modifying the graph as shown in Figure 3 and
calculate the probabilities following Equation 3. Thus, we only need to re-construct the probability tables for P(F), P(A|F)
and P(B|D,F).
Figure 3: Incorporating New Variables in Existing Bayesian Network
(3)
Lastly, let us assume that each of these variables has two states and they are represented with small letters (e.g., state of
A as a1 and a2). Now, we would like to predict the probability of C being in c2 state when we have information about only A
D and E (A = a1, D = d2 and E = e1). This can be obtained by using Baye's theorem by marginalizing the variables as
presented with Equation 4.
(4)
Thus, BN has inherent capability to update the model in real-time, revise the model with partial new data, incorporate
new variables by updating the probability tables of other variables directly connected to the new variables and make
inferences even when information regarding all the variables are not available; which are the major qualities required in a
suitable method for real-time crash prediction. In the next section, we have investigated if BN can produce satisfactory
results in case of crash prediction as compared to the well known method to predict dichotomous outcome – the Binary
Logistic Regression method.
4. Model Building and Performance Evaluation
The model building process consists of four major steps. At first, we artificially generated a dataset for crash prone and
normal traffic condition, then we separately built two models, one with BN and the other with Binary Logistic Regression,
then we evaluated their performance separately and lastly, we tested if BN could predict crashes as well as the model with
Binary Logistic Regression. The work flow followed to compare Logistic Regression and Bayesian Network in this study is
presented in Figure 4. The study is a framework study by nature and the data used are statistically simulated. It is
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understandable that the data may not represent real world situation properly. Thus, the study is not concerned with the
phenomena of crash prone and normal traffic conditions, rather, the study asks the question, 'If the data are like this, then
can BN predict crashes as well as the widely accepted Binary Logistic Regression?'. Being a real-time prediction model, BN
has advantages over Binary Logistic Regression in suitability for real-time crash prediction. This section investigates if its
prediction capability is also acceptable considering Binary Logistic Regression as the bench mark.
Figure 4: Work flow of the study
(1) Data Preparation
In this study, we have used artificially generated data using the descriptive statistics of real-time traffic flow data
provided by Oh et al. 2,3). In their studies, they obtained data from loop detectors installed on a 15.3 kilometers four to five
lane straight section of the I-880 freeway in Hayward, California from February 16 through March 19, 1993 which was
stored by the authority. They eliminated the impact of road geometry by choosing the section with uniform road geometry.
They focused on the data during the peak period (5 am to 10 am and 2 p.m. to 7 p.m.) as both possibilities and consequences
of road crashes during the peak period are the highest. For the model building purpose, the separated the data into two parts
– disrupted or hazardous traffic condition and normal traffic condition. The defined normal traffic condition as a 5 minute
period, 30 minute prior a crash and disrupted traffic condition as a 5 minute period just prior crash. Later, they aggregated
the detector data for each 10 seconds and then calculated the mean and the standard deviation of aggregated speed, flow and
occupancy for the 5 minute period to obtain the model predictors. However, the found significant pattern difference between
hazardous and normal traffic conditions only in case of the standard deviation of the aggregated data. In their study, they
provide these descriptive statistics of standard deviation of speed, flow and occupancy of 10 minute aggregated data for the
5 minute period accompanied with their plots of their distributions (see Figure 5) as well as the results of t-test (see Table 2).
Table 2: Descriptive statistics of standard deviation of speed, flow and occupancy
10 second detector data aggregated for 5 minutes
Category
Mean
Std. Dev.
t-stat.
Std. Dev. of Speed*
Std. Dev. of Flow*
Std. Dev. of Occupancy*
Disrupted
Normal
Disrupted
Normal
Disrupted
Normal
3.66
2.77
3.84
3.37
3.46
3.08
1.52
1.3
0.9
0.83
1.46
1.72
4.94
-3.68
1.87
* see the explanation section within Figure 5 for the units of the variables
Considering the other previous research studies on real-time crash prediction, it can be understood that the most
significant variables had been the aggregated descriptive statistics (hear mean and standard deviation) form of 'Flow',
'Speed' and ‘Occupancy’ – which can be easily obtained from the basic outputs of most of the real-time traffic data
collection equipments. Moreover, these three variables are considered sufficient to explain the traffic condition on roads as
well. From Table 2 and Figure 5, we can understand that the standard deviation of the aggregated speed, flow and
occupancy data roughly follow a bell shaped curve for both disrupted and normal conditions. Thus, for our study, we used
these statistical values to generate our datasets.
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Figure 5: Distribution of Standard Deviation of Speed, Flow and Occupancy of Oh et al. 1-3)'s Data
Source: Oh et al. 3)
We used built in function of the R-Package (Dalgaard10)) to simulate the data and assuming normal distributions using
the parameters in Table 2. The simulation time period was one year – 12 hours a day, 5 days a week and 52 weeks a year.
The data were then aggregated for each 5 minute period (following Oh et al. 2,3)) and we assumed that disrupted traffic
conditions are best defined by the 5 minute traffic condition prior to a crash and the rest of the time periods are normal
traffic conditions. In case of crashes, we assumed that 10 crashes occur every week day in the simulated study section (can
be assumed as a relatively long section) through out the year. Thus, we obtained 2600 (10 X 5 X 52 = 2600), 5 minute
aggregated data points of standard deviation of speed, flow and occupancy for traffic conditions causing crashes or near
miss crashes. Similarly, we simulated 34840 (12 X 12 X 5 X 52 – 2600 = 34840) data points for the normal traffic condition.
Lastly, we assigned a value of '1' with each data point of the crash or near miss crash dataset and '0' for the normal traffic
condition dataset. Figure 6 presents the box plots of the three variables (explanation provided within the figure): 5 minute
standard deviation of speed, flow and occupancy. Here '1' represents disrupted traffic condition and '2' represents normal
traffic condition. The boxes in the figure represents the inter quartile distance and the middle bold horizontal like represents
the median and the cross represents the mean value of the generated data. Comparing Table 2 and Figure 6, we can
understand that the artificially generated dataset follows normal distribution with means close to the corresponding values
mentioned in Table 2.
(2) Modeling with Bayesian Network
The first step in BN modeling involves identifying a hypothesis variable where each of its states (mutually exclusive
and collectively exhaustive) will be defined. The next step involves identification of the predictors for the hypothesis
variable, normally referred as information variable. In this study, the hypothesis variable is 'Crash' with two states – 'Yes'
and 'No', where ‘Yes’ represents both crash and near miss crash situations. This is a dichotomous variable providing
information regarding the instantaneous crash risk based on predictor data. Here, the previously mentioned standard
deviation of 10 second aggregated values of speed, flow and occupancy for the duration of 5 minutes are chosen as the
information variables and are represented as SSD5, FSD5 and OSD5. The next step requires finalizing the graph where the
information variables are linked with the hypothesis variables – directly or indirectly. In our case, there can be two potential
possibilities for the Bayesian Network as presented in Figure 7 (a) and (b). We did not find high correlation among the
information variables and therefore, did not provide any direct links among them. In Figure 7, SSD5, FSD5 and OSD5 are
called the parent nodes of ‘Crash’ connected with a converging connection (a) or child node of 'Crash' connected with a
diverging connection (b). The converging connection in this situation has potential advantage over the diverging connection
as it facilitates flow of inference among the information variables when hard or soft evidence about ‘Crash’ is available. It
means that in case of Figure 7(b), if information regarding whether a crash or near-miss crash has taken place is known,
then information regarding SSD5 does not have any impact on our belief regarding FSD5 or OSD5 and vise versa. However,
the model in Figure 7(a) can be used to understand the inter-relationship among all these variables during crash. To
elaborate, any information about ‘Crash’ and any of the information variables will have influence on the belief regarding the
other two information variables. This characteristic of Bayesian Network is termed as the ‘explaining away effect’ or
sometimes the ‘bi-directional inference’.
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Figure 6: Box plot of statistically simulated data (1=Disrupted, 2=Normal traffic condition)
(Units are as explained in Figure 5)
(a)
(b)
Figure 7: Potential Bayesian Networks
Now, using the universal probability distribution of Bayesian Network (see Equation 1), the probability of any state of
any variable can be calculated from the universe of probability distribution P(U) = P(Crash, SSD5, FSD5, OSD5) as
presented in Equation (5).
(5)
In the next step, we create the probability tables for each node in the BN. In our model, data for each information
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variable (standard deviation of speed, flow and occupancy) were classified into smaller groups and their frequency
distribution was calculated as presented in Table 3. This was done to facilitate producing the probability distribution tables
for the information variables. Now a days, BN can handle continuous data, however, it requires a substantial amount of time
for modeling, which can be saved through careful discritization of the continuous data into smaller groups. The
classification process went through rigorous trials in order to find separate suitable class intervals for each of the
information variables which will not compromise with the accuracy of the model but reduce the number of categories for
each variable and thus reduce the calculation time.
Table 3: Prior probability distribution
5 minute aggregated standard deviation of
Speed
Flow
Occupancy
Category P(Speed) Category P(Flow) Category P(Occupancy)
<=1
0.08 <=2.5
0.08
<=1
0.08
1.5
0.08
3
0.12
1.5
0.06
2
0.11
3.5
0.18
2
0.09
2.5
0.14
4
0.21
2.5
0.11
3
0.15
4.5
0.19
3
0.13
3.5
0.14
5
0.13
3.5
0.13
4
0.12
5+
0.1
4
0.12
4.5
0.08
4.5
0.1
5
0.05
5
0.07
5+
0.05
5+
0.1
Afterwards, the process in BN updates the conditional probability tables of each child node by calculating their posterior
probabilities based on the information on the prior probabilities of the parents and the node itself using the well known
Baye's theorem. This process is complex and the calculation is time consuming. For this, we used limited version of Netica
(http://www.norsys.com/), a popular commercial package to develop models with Bayesian Network, to build our prototype
the real-time crash prediction model. For this, we connected the three information variables using a converging connection
to the hypothesis variable named 'Crash'. This process proceeded by entering the prior probabilities of the information
variables and the conditional probability tables for the variable 'Crash' (i.e., probability of crash based on different
combinations of standard deviation of speed, flow and occupancy; P(Crash|SSD5, FSD5, OSD5) and building of the model.
The prior probability of each variable when no prior information regarding any variable is available is presented in Figure 8.
The outcome of the Bayesian Network suggests that based on the data, the average risk of crash or near miss crash for the
road section is 6.89%, i.e., when no other information is available, there is a 6.89% chance that a crash or a near miss crash
can occur at the road section during peak hour of a weekday.
Figure 8: Bayesian Network Model
As mentioned in Section 3, the probability of the universe in a Bayesian Network can be represented only with the
parent nodes and the conditional probability of the child nodes given their immediate parent nodes. Thus, when we obtain
new findings e = {S_SD5, F_SD5, O_SD5} in real-time through traffic data sensing equipment, we can calculate the
probability of crash using Bayes rule as shown in Equation (6).
(6)
Here, we can calculate P(e) by marginalization of the universal probability distribution P(U) (see Equation 4, too). This
empowers BN with the ability to coordinate bi-directional inferences, which is difficult to achieve with conventional
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statistical approaches. For example, in this prototype model we have used the BN to predict the probability of crashes based
on available data. However, the same model can be used to predict the probability of SSD5 or FSD5 or OSD5 when data
about crash and one of these three information variables become available. Thus, the same model can be used to understand
what kinds of combinations of standard deviations of speed, flow and occupancy have high likelihood to cause road crashes.
(3) Modeling with Logistic Regression
As we have already separated the artificially generated data into two categories (crash or near miss crash condition and
normal condition), we could build a Binary Logistic Regression model based on that. We used R-package for this purpose,
too. The results are as presented in Table 4.
Coefficient
Pr( >|z|)
Sig. Code
Deviance
Table 4: Results of the logistic regression model
(intercept)
Std. Dev. of Occupancy
Std. dev. of Flow
Std. dev. of Speed
-2.89958
0.1797
-0.53475
0.51098
<2e - 16 ***
<2e - 16 ***
<2e - 16 ***
<2e - 16 ***
*** 0.001, ** 0.01, * 0.05
Null: 18885 on 37439 degrees of freedom
Residual: 17073 on 37436 degrees of freedom
(4) Performance Evaluation
The last step of the study we conducted a random sampling of 50 data points, each from both the simulated data points
of normal and disrupted traffic condition and tested the results with the newly developed models following previous studies
that compared Logistic Regression and Bayesian Network 11). For this, we calculated the probability of crash for each data
point and classified it as crash if the value is over 6.98%, which is the average crash risk for the simulated data (see Figure
6). In real life scenario, the choice of the threshold will be a more complex activity as measures involved with reducing the
crash risk is cost dependent and the authorities need to judge the threshold value after carefully conducting the cost-benefit
analysis. However, in our case, the concern is to assess if BN can predict crash properly by taking the prediction capability
of the Binary Logistic Regression model as the standard. The outcome of the validation process is presented in Table 5.
From this, it can be realized that both the developed models show similar level of accuracy in predicting non-crash situation
whereas the BN based model was 18% more successful (Binary Logistic Regression and BN successfully predicted 37 and
28 crash cases respectively out of 50 evaluation samples) in identifying crash or near-miss crash situations than the Logistic
Regression based model. We did not conduct any further statistical test as our interest was to investigate if BN can predict as
closely as the Binary Logistic Regression model or not.
Actual
Table 5: Performance evaluation
Predicted
Bayesian Network
Logistic Regression
Crash
Non-Crash
Crash
Non-Crash
37
13
28
22
Crash
14
36
16
34
Non-Crash
5. Discussion and Conclusion
The idea of predicting crash in real-time is very new and it is still in the conceptual level. Its modeling methods have
some additional special requirements due to resource constrains. For example, an applicable model requires to be developed
based on sufficient amount of data, however, crash is a rare event and in many occasions, it is difficult to obtain crash data
of good quality and quantity. Moreover, real-time crash prediction models require reliable real-time traffic flow data, which
were hard to obtain until recently. At times, the model can get erroneous if the reported crash time does not match with the
actual crash time. For this, these models should be built with high flexibility where the model can be calibrated in regular
interval as new data become available in course of time. Moreover, most of the basic real-time models developed so far do
not consider the impact of weather and eliminate the impact of road geometry by choosing homogeneous road sections. For
a practical model, in future, it is expected to have capabilities to incorporate new predictors into the model without needing
to collect data for all the predictors. In many cases, the time of data collection for different predictors may be different, too.
Apart from these, the model needs to be capable of making inference with partial data as many times detectors fail to
provide reliable data for all the variables. The model also needs to predict fast to provide buffer time to take necessary
actions to acerbate the risk of crash. Thus, the requirements of a real-time crash prediction modeling method can be
classified into three broad groups – a) flexibility in model calibration (both with the availability of new data and new
predictors) b) speed in prediction c) accuracy of the model. However, the current attempts on real-time crash prediction are
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highly concentrated on how to increase the prediction capability, ignoring the former two requirements. In this paper, we
have emphasized that an actionable real-time crash prediction model needs to concentrate on settling for a method that
satisfies all these three needs rather than the accuracy of the model only. In this paper, after explaining the current
developments and requirements for a real-time crash prediction model (see Section 2), we have explained the inherent
capability of BN in updating the model in real-time, incorporating new variables, making inferences with minimum
calculation; which makes it a highly suitable method for real-time prediction. Apart from these, BN has some other extra
advantages over many of its competing statistical models. For example, BN is a non-parametric modeling approach and we
do not need to store previous data for each time we update a BN, rather, we just store the probability tables of each node and
update the probabilities with the new data using Baye's theorem. However, in case of statistical models like Binary Logistic
Regression, we either need to store the previous data or need to apply complex Bayesian statistics based approaches to
update the models regularly, which can be substantially resource hungry.
However, even after having these capabilities, it was important to ensure that BN can also conduct predictions with
acceptable level of accuracy. For this, we have chosen the prediction capability of Binary Logistic Regression, a well known
method for predicting dichotomous outcomes in the field of statistics as well as transportation engineering, as the bench
mark and evaluated the prediction capability of BN thereby. For this, we used simulated data from previous studies (Oh et al.
2,3)
). It can be understood that the simulated data may not represent an actual situation properly; however, our interest was
confined within evaluating the prediction performance of BN with respected Binary Logistic Regression, assuming that the
simulated data are a representation of actual real-time traffic flow data. The outcome of the study suggests that Bayesian
Network based model could predict crash situations with 18% higher accuracy than the Binary Logistic Regression based
model for the simulated data, although, the performances to predict non-crash prone situations were relatively identical
(68% for Logistic Regression and 72% for BN). Real-time crash prediction is a new branch of proactive road safety
management systems with high promise. So far, the research development in this field is limited within the process of
establishing a framework and none of the previous models have been implemented in real-life situation. This paper is a part
of an ongoing research study on the development of a real-time crash prediction model for urban expressways of Japan,
which is being carried out in Tokyo Institute of Technology, Japan. At present, using the findings of this paper, we have
developed a basic real-time crash prediction model using Bayesian Network for Japanese urban expressways using real-time
detector data and expect to excel the study to develop a model that can be implemented in practical situation in near future.
References
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Research Board, 2001.
2) Oh, J., Oh, C., Ritchie, S., and Chang, M. Real time estimation of accident likelihood for safety enhancement. ASCE Journal of
Transportation Engineering, Vol. 131, No. 5, pp 358-363, 2005.
3) Oh, C., Oh, J., Ritchie, S., and Chang, M. Real time hazardous traffic condition warning system: framework and evaluation, IEEE
Journal of Intelligent Transportation Systems, Vol.6. No.3, pp 265-272,2005.
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7) Abdel-Aty, M., and Abdalla, M. F. Linking roadway geometrics and real-time traffic characteristics to model daytime freeway crashes
using generalized estimating equations for correlated data. Journal of Transportation Research Board, No.1897, 2003.
8) Luo, L., and Garber, N. J. Freeway Crash Prediction Based on Real-Time Pattern Changes in Traffic Flow Characteristics. Project
Report for the ITS Implementation Center, UVA Center for Transportation Studies. Research Report No. UVACTS-15-0-101, 2006.
9) Jensen, F. V. and Nielsen, T. D. Bayesian network and decision graphs.2nd Ed., Springer, New York, USA, 2007.
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diagnosis of breast cancer. Proceedings of the 28th Annual Meeting of the Society for Medical Decision Making, 2006, USA.
A Framework for Real-time Crash Prediction: Statistical Approach versus Artificial Intelligence*
by Moinul HOSSAIN** and Yasunori MUROMACHI**
This paper evaluates the possibility of Bayesian Network to predict road crash risks in real-time. Two data sets, one for
normal traffic conditions and another for conditions leading to crash were statistically generated based on previous studies.
Two separate crash prediction models were developed, (logistic regression and Bayesian Network) followed by their
performance evaluation by randomly drawing 50 samples and comparing their computed and actual outcome. The results
suggest similar prediction success for non-crash situations, whereas, the model based on Bayesian Network predicted crashprone conditions 18% more accurately than the Logistic Regression based model.
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